Added parking warm-up

Misc/Warm-Ups/parking.tex

@@ -0,0 +1,83 @@
+\documentclass[
+	solutions,
+	shortwarning,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+\geometry{top = 20mm}
+
+\title{Warm-Up: Parking Problems}
+\subtitle{Prepared by \githref{Mark} on \today.}
+
+\begin{document}
+
+	\maketitle
+
+
+
+	\problem{A Minor Inconvenience}
+	A group of eight friends goes out to dinner. Each drives his own car, checking it in with valet upon arrival.
+	Unfortunately, the valet attendant forgot to tag the friends' keys. Thus, when the group leaves the restaurant,
+	each friend is handed a random key.
+	\begin{itemize}
+		\item What is the probability that everyone gets the correct set of keys?
+		\item What is the probability that each friend gets the wrong set?
+	\end{itemize}
+
+	\vfill
+
+
+	\problem{Bimmer Parking}
+	A parking lot has a row of 16 spaces, of which a random 12 are taken. \par
+	Ivan drives a BMW, and thus needs two adjacent spaces to park. \par
+	What is the probability he'll find a spot?
+
+	\vfill
+	\pagebreak
+
+
+	\problem{Petty Bruins in Westwood}
+	Suppose 6 students live on a one-way street which features six parallel parking spaces.
+	Each student has their favorite spot, and will always check if that spot is free.
+	If it is, they will park there. If it isn't, they will take the next free spot.
+	Backing up is not an option.
+
+	If each student chooses a \say{favorite} spot independently and at random...\par
+	\begin{itemize}
+		\item what is the probability that each student has a different favorite spot?
+		\item what is the probability that all six people will park successfully?
+	\end{itemize}
+
+
+
+	\vfill
+
+
+
+	\problem{Ship Packing}
+	A certain harbor services ships that are exactly 10 meters long.
+	These ships are equipped with transverse thrusters, and thus have
+	no problem parking in parallel (a ship may fit in any gap that is
+	at least 10 meters long).
+
+	\vspace{2mm}
+
+	There is an empty 100-meter span where these ships may be parked in parallel.
+	Parking spaces are not marked---ships may pick a parking spot anywhere on this
+	continuous 100-meter length.
+
+	\vspace{2mm}
+
+	As ships arrive, they pick a random available spot along this span. \par
+	How many ships do we expect to fit on this 100-meter region?
+
+	\hint{This problem is difficult, start with simpler cases.}
+
+
+
+	\vfill
+	\pagebreak
+
+
+\end{document}